To introduce notation and background, we consider a
a graph \(G=(V,E)\) , with \(N=|V|\)  number of nodes and \(M=|E|\)  as the number of edges.
The standard
centrality measure most relevant to our work is
betweenness (shortest path betweenness), [1]}.
For a node \(v\) , this measure is defined as
\(b_v = \sum _{i\ne j\ne v}\frac{\sigma _{i,j}\left( v \right)}{\sigma _{i,j}}\) 
